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3 years ago

Given the numbers 36 60 and 72 write the numbers as a product of their prime factors

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

6 0

Answer:

36:2 times 2 times 3 times 3.

60:2 times 2 times 3 times 5

72:2 times 2 times 2 times 3 times 3

Step-by-step explanation:

just keep in mind that when it says times it means multiplication sign.

hope this helps

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The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 2 i

Marrrta [24]

Answer:

Rate of change of volume when the radius is 40 inches and the height is 20 inches = 0 inch³/s

Step-by-step explanation:

We have

$\texttt{Volume = }\frac{1}{3}\pi r^2h$

Taking derivative with respect to time,

$V=\frac{1}{3}\pi r^2h\\\\\frac{dV}{dt}=\frac{1}{3}\pi \frac{d}{dt}\left (r^2h \right )\\\\\frac{dV}{dt}=\frac{1}{3}\pi \left ( 2r\frac{dr}{dt}\times h+r^2\frac{dh}{dt}\right)$

Given that

r = 40 inches

h = 20 inches

$\frac{dr}{dt}=2inch/s\\\\\frac{dh}{dt}=-2inch/s$

Substituting

$\frac{dV}{dt}=\frac{1}{3}\pi \left ( 2r\frac{dr}{dt}\times h+r^2\frac{dh}{dt}\right)\\\\\frac{dV}{dt}=\frac{1}{3}\pi \left ( 2\times 40\times 2\times 20+40^2\times (-2)\right)\\\\\frac{dV}{dt}=\frac{1}{3}\pi \left (3200-3200\right)=0inch^3/s$

Rate of change of volume when the radius is 40 inches and the height is 20 inches = 0 inch³/s

4 0

3 years ago

Which ordered pair is the solution to the system of linear equations y = negative 7 x + 2 and y = 9 x minus 14? (negative 5, 1)

Anettt [7]

Answer:

B. $(1,-5)$

Step-by-step explanation:

We have been given a system of equations. We are asked to choose the ordered par that is the solution to the given system.

$y=-7x+2...(1)$

$y=9x-14...(2)$

To solve our given system, we will equate both equations as:

$9x-14=-7x+2$

Combine like terms:

$9x+7x-14+14=-7x+7x+2+14$

$16x=16$

$x=\frac{16}{16}=1$

Upon substituting $x=1$ in equation (1), we will get:

$y=-7(1)+2\\\\y=-7+2\\\\y=-5$

Therefore, the ordered pair $(1,-5)$ is the solution of the given system and option B is the correct choice.

7 0

3 years ago

Read 2 more answers

Rounded 16,500 to the nearest ten thousand

cricket20 [7]

The nearest ten thousand to 16,500 is 20,000. So it is rounded up to 20,000.
Because 16,500 is more nearest to 20,000 than 10,000, a the second digit after 1 is 6 which is greater than 5 and close to 10 than 1. if it is less than 5, for example if the number is 14,500 then the number will be rounded to 10,000 as that one is more closest than 20,000.
But here 16,500 is rounded to 20,000.

3 0

3 years ago

Solve :1/1-x^a-b +1/1-x^b-a

Stolb23 [73]

The answer to the above eqaution is 1

Step-by-step explanation:

Proceeding step by step

Step 1= 1/(1-xᵃ⁻ᵇ)+ 1/(1-xᵇ⁻ᵃ)

on rearranging the equation (b-a) as -(a-b) and substituting the value

Step 2= 1/(1-x ᵃ⁻ᵇ) + 1/(1-x -⁽ᵃ⁻ᵇ⁾ )

Using the indices corrolary that 1/1- x ⁻ᵃ= -xᵃ/ (1- x ᵃ) and subsituting the value of the expression in the step mentioned below

Step 3=1/(1+x ᵃ⁻ᵇ) - (x ᵃ⁻ᵇ)/(1-x ᵃ⁻ᵇ)

Since the denominators are the same the two fractions can be added with common denominator being 1+x ᵃ⁻ᵇ

On adding the above mentioned step 3 we get

Step 4=(1- x ᵃ⁻ᵇ) / (1- x ᵃ⁻ᵇ)

Thus the value of equation =1

4 0

3 years ago

What Will be plant height likely be on August 1

andrew11 [14]

Answer:

Step-by-step explanation:

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3 years ago

Given the numbers 36 60 and 72 write the numbers as a product of their prime factors​

Given the numbers 36 60 and 72 write the numbers as a product of their prime factors